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Endochronic Fatigue Life Prediction of SN/3.5AG/0.75CU BGA Solder Joints Under Oblique Displacement Cyclic Tests

Published online by Cambridge University Press:  16 June 2011

C. F. Lee ,
T. T. Lin  and
P. S. Tsai
C. F. Lee*
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
T. T. Lin
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
P. S. Tsai
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Professor, corresponding author
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Abstract

In this paper, cyclic damage behavior of cyclically load drop curves and their fatigue initiation life of Sn/3.5 Ag/0.75Cu BGA solder joint specimens under oblique displacement cyclic tests were investigated by the theory of damage — coupled endochronic viscoplasticity.

By linearly unloading with damage elastic modulus and the linearly damage-free behavior of grip system, the damage loops of force-Φ angle oblique displacement of BGA solder joint specimen were converted successfully into damage loops of the representative solder ball under cyclically proportional straining, which can be predicted by the endochronic constitutive equations. These results established the relationship of the BGA oblique displacement amplitudes da(Φ) and the effective inelastic strain amplitudes of solder ball: da (Φ)= . Based on the phenomena of cyclic damage and its fatigue life, a Φ dependent degree of damage in the evolution equation of damage under proportional strain path was proposed to depend positively on and N cycles. Using this parameter in the damage per cycle computed by the endochronic theory, a Φ modified cycles N(Φ)/β(Φ) can be defined and then derive the Φ modified Lee-Coffin-Manson (Φ-LCM) equation for the fatigue initiation life of solder ball:

Finally, a Φ modified Lee's BGA (Φ LBGA) equation for BGA solder joint specimens can be derived:

This equation can predict quite well the life data of Sn/3.5Ag/0.75Cu solder joint specimens under Φ ϵ [0π/2]. As a consequence, a vehicle to study the fatigue initiation life of BGA solder joint specimens is constructed completely by the workable methodology and the theory discussed in the paper.

Keywords

Damage-coupled endochronic viscoplasticitySn/3.5Ag/0.75Cu BGA solder joint specimenΦ angle oblique displacement cyclic testΦ-LCM & Φ LBGA fatigue life equationsDamage evolution equation
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. 191 - 200
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

1. Lee, C. F. and Shieh, T. J., “Theory of Endochronic Cyclic Viscoplasticity of Eutectic Tin/Lead Solder Alloy,” Journal of Mechanics, 22, pp. 181–191 (2006).Google Scholar
2. Stolkarts, V., Keer, L. M. and Fine, M. E., “Constitutive and Cyclic Damage Model of 63Sn/37Pb Solder,” Journal of Electronic Packaging, ASME, 123, pp. 351–355 (2001).CrossRefGoogle Scholar
3. Lee, C. F. and Chen, Y. C., “Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity with Damage-Application to Eutectic Sn/Pb Solder Alloy,” Journal of Mechanics, 23, pp. 433–444 (2007).CrossRefGoogle Scholar
4. Lee, C. F. and Lee, Z. H., “Predicting Fatigue Initiation Life of Sn/3.8Ag/0.7Cu Solder using Endochronic Cyclic Damage-Coupled Viscoplastic Theory,” Journal of Mechanics, 24, pp. 369–377 (2008).CrossRefGoogle Scholar
5. Vaynman, S., Fine, M. E. and Jeannotle, D. A., “Low-Cycle Isothermal Fatigue Life of Solder Materials,” Solder Mechanics, Frear, et al. , Eds., The Minerals, Metals & Materials Society, pp. 169–184 (1991).Google Scholar
6. Chen, X., Song, J. and Kim, K. S., “Low Cycle Fatigue Life Prediction of 63Sn-37Pb Solder under Proportional and Non-Proportional Loading,” International Journal of Fatigue, 28, pp. 757–766 (2006).CrossRefGoogle Scholar
7. Park, T. S. and Lee, S. B., “Low Cycle Fatigue Testing of Ball Grid Array Solder Joints Under Mixed-Mode Loading Conditions” Journal of Electronic Packaging, ASME, 127, pp. 237–244 (2005).CrossRefGoogle Scholar
8. Lee, C. F., Lee, T. K., Lin, T. T. and Lin, H. Y., “Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Obligue Displacement Tests and Endochronic Viscoplastic Predictions,” Journal of Mechanics, 26, pp. 453–463 (2010).Google Scholar
10. Endo, T. and Morrow, J., “Cyclic Stress-Strain and Fatigue Behavior of Representative Aircraft Metals,” Journal of Material, 4, pp. 159–175 (1969).Google Scholar
11. Socie, D. F., Waill, L. A. and Dittmer, D. F., “Biaxial Fatigue of Inconel 718 Including Mean Stress Effects,” Multiaxial Fatigue, ASTM STP 853, Miller, K. J. and Brown, M. W., Eds., American Society for Testing and Materials, Philadelphia, pp. 463–481 (1985).CrossRefGoogle Scholar
12. Kandil, F. A., Brown, M. W. and Miller, K. J., “Biaxial Low-Cycle Fatigue Fracture of 316 Stainless Steel of Evaluated Temperatures,” Mechanical Behavior and Nuclear Applications of Stainless Steel at Elevated Temperatures, Book 280, The Metals Society, London, pp. 203–210 (1982).Google Scholar